Applied Complex Variables

一般大眾初學者以淺顯圖文介紹最新都市規劃科學的內涵都市規劃是一門正在演進的學科，然而學界及業界中相對少的人認識到這是一門科學。這本書彙整了作者過去35年來的研究成果，從複雜學的觀點以相對淺顯的圖文來說明都市規劃科學的內涵。自從2019年底新冠肺炎疫情席捲全球的都市後，正顯示出只有人們才是都市的靈魂，沒有考慮「人」的都市規劃是落空的。本書所介紹的都市規劃科學便是以「人」為出發點，探討社會科學針對人類選擇行為的解釋與自然科學針對複雜系統的理解，並將兩者整合成一系統性的都市規劃現象的描述與解釋。2021年諾貝爾物理學獎頒給三位從事複雜系統研究的學者，正說明了複雜學已獲得最高學術殿堂的認可。希望本書的出版能對有志探索人類如何面對都市複雜性的學術或專業規劃師有所幫助。■ 自序現代科學正進行著一場顛覆性的複雜性運動或革命，而這個運動或革命正在或已經影響了社會科學及自然科學許多領域的發展，包括都市規劃。因此，學界對都市及規劃的理解也產生了變化：都市不再是簡單的均衡系統，而是複雜的非均衡系統；規劃從過去強調空間、共識及控制的靜態描述轉而著重時間、結盟及計畫的動態過程(Hopkins, 2014)。此外學者也認為應用大數據及數位孿生的電腦科技從事都市規劃，仍然離不開以複雜性科學來理解都市的理論。尤有甚者，筆者在2018 年發現了四個I 與規劃作用及複雜性的邏輯關係，將規劃的概念與複雜性科學聯繫起來。四個I 表示都市發展決策的相關性(Interdependence)、不可逆性(Indivisibility)、不可分割性(Indivisibility) 以及不完全預見性(Imperfect Foresight)( 詳見本書第三章第五節)。具體而言，規劃發生作用為四個I 的充分條件，而四個I 又是複雜性的充分條件，因此規劃發生作用是複雜性的充分條件(Lai, 2018)。用一般的話來講，計畫在複雜系統中發生作用，但不是唯一的方式。這個發現也確立了四個I 與規劃及複雜度的關係；亦即四個I 同時是規劃投資及複雜度的指標，而這個邏輯關係貫穿了本書的理論架構。我書Planning within Complex Urban Systems (Lai, 2021) 及其姊妹作《複雜城市系統中的規劃原理：新觀點、新邏輯與新實驗》( 賴世剛，2022) 系統地整理了筆者過去35 年來的核心研究心得，以完整

The central theme of this reference book is the metric geometry of complex analysis in several variables. Bridging a gap in the current literature, the text focuses on the fine behavior of the Kobayas

Applied Theatre: Creative Ageing examines the complex social, political and cultural needs of a diverse group in our society and asks how contemporary applied theatre responds to those needs. For the

We live in a complex and dynamic world. Understanding how to monitor, manage and conserve species and habitats--the goal of applied ecology--is becoming increasingly important. Applied Ecology shows s

Complex software systems have been designed to efficiently handle large numbers of variables. In manufacturing, variables affect every part of the supply chain from inventory to production to delivery

Complex software systems have been designed to efficiently handle large numbers of variables. In manufacturing, variables affect every part of the supply chain from inventory to production to delivery

This volume includes 28 chapters by authors who are leading researchers of the world describing many of the up-to-date aspects in the field of several complex variables (SCV). These contributions are

This book investigates several classes of partial differential equations of real time variable and complex spatial variables, including the heat, Laplace, wave, telegraph, Burgers, Black–Merton–Schole

In response to the exponentially increasing need to analyze vast amounts of data, Neural Networks for Applied Sciences and Engineering: From Fundamentals to Complex Pattern Recognition provides scient

Complex Analysis and Applications, Second Edition explains complex analysis for students of applied mathematics and engineering. Restructured and completely revised, this textbook first develops the t

Multivariate analysis plays an important role in the understanding of complex data sets requiring simultaneous examination of all variables. Breaking through the apparent disorder of the information,

This book provides practical guidance on research methods and designs that can be applied to Complex Dynamic Systems Theory (CDST) research. It discusses the contribution of CDST to the field of appli

This practical book is designed for applied researchers who want to use mixed models with their data. It discusses the basic principles of mixed model analysis, including two-level and three-level structures, and covers continuous outcome variables, dichotomous outcome variables, and categorical and survival outcome variables. Emphasizing interpretation of results, the book develops the most important applications of mixed models, such as the study of group differences, longitudinal data analysis, multivariate mixed model analysis, IPD meta-analysis, and mixed model predictions. All examples are analyzed with STATA, and an extensive overview and comparison of alternative software packages is provided. All datasets used in the book are available for download, so readers can re-analyze the examples to gain a strong understanding of the methods. Although most examples are taken from epidemiological and clinical studies, this book is also highly recommended for researchers working in other

This practical book is designed for applied researchers who want to use mixed models with their data. It discusses the basic principles of mixed model analysis, including two-level and three-level structures, and covers continuous outcome variables, dichotomous outcome variables, and categorical and survival outcome variables. Emphasizing interpretation of results, the book develops the most important applications of mixed models, such as the study of group differences, longitudinal data analysis, multivariate mixed model analysis, IPD meta-analysis, and mixed model predictions. All examples are analyzed with STATA, and an extensive overview and comparison of alternative software packages is provided. All datasets used in the book are available for download, so readers can re-analyze the examples to gain a strong understanding of the methods. Although most examples are taken from epidemiological and clinical studies, this book is also highly recommended for researchers working in other

The Little Quick Fix on how to Identify Your Variables unlocks the gate to simple data analysis for any stats course. Packed with lively examples it shows students what variables a

This volume sheds light on the current state of complex networks and nonlinear dynamics applied to the understanding of economic and social phenomena ranging from geographical economics to macroeco

As most econometricians will readily agree, the data used in applied econometrics seldom provide accurate measurements for the pertinent theory's variables. Here, Bernt Stigum offers the first systema

The monograph is devoted to integral representations for holomorphic functions in several complex variables, such as Bochner-Martinelli, Cauchy-Fantappie, Koppelman, multidimensional logarithmic resid

The majority of empirical research in economics ignores the potential benefits of nonparametric methods, while the majority of advances in nonparametric theory ignore the problems faced in applied econometrics. This book helps bridge this gap between applied economists and theoretical nonparametric econometricians. It discusses in depth, and in terms that someone with only one year of graduate econometrics can understand, basic to advanced nonparametric methods. The analysis starts with density estimation and motivates the procedures through methods that should be familiar to the reader. It then moves on to kernel regression, estimation with discrete data, and advanced methods such as estimation with panel data and instrumental variables models. The book pays close attention to the issues that arise with programming, computing speed, and application. In each chapter, the methods discussed are applied to actual data, paying attention to presentation of results and potential pitfalls.

The majority of empirical research in economics ignores the potential benefits of nonparametric methods, while the majority of advances in nonparametric theory ignore the problems faced in applied econometrics. This book helps bridge this gap between applied economists and theoretical nonparametric econometricians. It discusses in depth, and in terms that someone with only one year of graduate econometrics can understand, basic to advanced nonparametric methods. The analysis starts with density estimation and motivates the procedures through methods that should be familiar to the reader. It then moves on to kernel regression, estimation with discrete data, and advanced methods such as estimation with panel data and instrumental variables models. The book pays close attention to the issues that arise with programming, computing speed, and application. In each chapter, the methods discussed are applied to actual data, paying attention to presentation of results and potential pitfalls.

This book explains and examines the theoretical underpinnings of the Complex Variable Boundary Element Method (CVBEM) as applied to higher dimensions, providing the reader with the tools for extending

Addressing a hugely diverse range of topics, both fundamental and applied, this anthology of papers from leading researchers in non-linear and complex dynamics honors the seminal contributions to the

This textbook provides engineers with the capability, tools and confidence to solve real-world heat transfer problems. It includes many advanced topics, such as Bessel functions, Laplace transforms, separation of variables, Duhamel's theorem and complex combination, as well as high order explicit and implicit numerical integration algorithms. These analytical and numerical solution methods are applied to topics not considered in most textbooks. Examples include heat exchangers involving fluids with varying specific heats or phase changes; heat exchangers in which axial conduction is a concern; and regenerators. Derivations of important results are presented completely, without skipping steps, which reduces student frustration and improves readability and retention. The examples are not trivial 'textbook' exercises; they are rather complex and timely real-world problems that are inherently interesting. This book integrates the computational software packages Maple, MATLAB®, FEHT and Eng

In this complete introduction to the theory of finding derivatives of scalar-, vector- and matrix-valued functions with respect to complex matrix variables, Hjørungnes describes an essential set of mathematical tools for solving research problems where unknown parameters are contained in complex-valued matrices. The first book examining complex-valued matrix derivatives from an engineering perspective, it uses numerous practical examples from signal processing and communications to demonstrate how these tools can be used to analyze and optimize the performance of engineering systems. Covering un-patterned and certain patterned matrices, this self-contained and easy-to-follow reference deals with applications in a range of areas including wireless communications, control theory, adaptive filtering, resource management and digital signal processing. Over 80 end-of-chapter exercises are provided, with a complete solutions manual available online.

Kapoor (U. of Hyderabad, India) finds the theory of functions of a complex variable to be one of those areas of mathematics that were created for reasons not even remotely connected to any practical,

Applied Metal Forming: Including FEM Analysis describes metal forming theory and how experimental techniques can be used to study any metal forming operation with great accuracy. For each primary class of processes, such as forging, rolling, extrusion, wiredrawing, and sheet-metal forming, it explains how FEA (Finite Element Analysis) can be applied with great precision to characterize the forming condition and in this way optimize the processes. FEA has made it possible to build very realistic FEM-models of any metal forming process, including complex three-dimensional forming operations, in which complex products are shaped by complex dies. Thus, using FEA it is now possible to visualize any metal forming process and to study strain, stresses, and other forming conditions inside the parts being manufactured as they develop throughout the process.

In recent years, scientists have applied the principles of complex systems science to increasingly diverse fields. The results have been nothing short of remarkable: their novel approaches have provid

This textbook provides engineers with the capability, tools and confidence to solve real-world heat transfer problems. It includes many advanced topics, such as Bessel functions, Laplace transforms, separation of variables, Duhamel's theorem and complex combination, as well as high order explicit and implicit numerical integration algorithms. These analytical and numerical solution methods are applied to topics not considered in most textbooks. Examples include heat exchangers involving fluids with varying specific heats or phase changes; heat exchangers in which axial conduction is a concern; and regenerators. Derivations of important results are presented completely, without skipping steps, which reduces student frustration and improves readability and retention. The examples are not trivial 'textbook' exercises; they are rather complex and timely real-world problems that are inherently interesting. This book integrates the computational software packages Maple, MATLAB®, FEHT and Eng

An intermediate-level text on the use of integral transforms in applied mathematics and engineering. Existing works either cover the subject in more elementary form or are advanced treatises. In a very lucid style the author deals with the use of this important mathematical tool to solve ordinary and partial differential equations in problems in electrical circuits, mechanical vibration and wave motion, heat conduction, and fluid mechanics. The book is divided into five parts covering integral transform pairs, the Laplace transform, Fourier transforms, Hankel transforms, and finite Fourier transforms. A basic knowledge of complex variables and elementary differential equations is assumed. There are many exercises and examples drawn from the above fields, tables of the transform pairs needed in the text, and a glossary of terms with which the student may be unfamiliar. For the student who seeks further background on the subject, an annotated bibliography is provided.

Detailing the main methods in the theory of involutive systems of complex vector fields this book examines the major results from the last twenty five years in the subject. One of the key tools of the subject - the Baouendi-Treves approximation theorem - is proved for many function spaces. This in turn is applied to questions in partial differential equations and several complex variables. Many basic problems such as regularity, unique continuation and boundary behaviour of the solutions are explored. The local solvability of systems of partial differential equations is studied in some detail. The book provides a solid background for others new to the field and also contains a treatment of many recent results which will be of interest to researchers in the subject.

Geared toward readers unfamiliar with complex numbers, this text explains how to solve the kinds of problems that frequently arise in the applied sciences, especially electrical studies. To assure an

The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure. The book starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more theoretical way than is usual in geometry. The author then proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The book culminates with the Hodge decomposition theorem. The meanings of these results are investigated in several directions. Completely self-contained, the book is ideal for students, while its content gives an account of Hodge theory and complex algebraic geometry as has been developed by P. Griffiths and his school, by P. Deligne, and by S. Bloch. The text is complemented by exercises which provide useful results in complex algebraic geometry.

Intended for engineering and math majors, this undergraduate textbook introduces the theory of complex numbers, defines transcendental functions of a complex variable, shows how evaluation of line int

As most econometricians will readily agree, the data used in applied econometrics seldom provide accurate measurements for the pertinent theory's variables. Here, Bernt Stigum offers the first systema

The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure. The book starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more theoretical way than is usual in geometry. The author then proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The book culminates with the Hodge decomposition theorem. The meanings of these results are investigated in several directions. Completely self-contained, the book is ideal for students, while its content gives an account of Hodge theory and complex algebraic geometry as has been developed by P. Griffiths and his school, by P. Deligne, and by S. Bloch. The text is complemented by exercises which provide useful results in complex algebraic geometry.

This user-friendly 1995 text shows how to use mathematics to formulate, solve and analyse physical problems. Rather than follow the traditional approach of stating mathematical principles and then citing some physical examples for illustration, the book puts applications at centre stage; that is, it starts with the problem, finds the mathematics that suits it and ends with a mathematical analysis of the physics. Physical examples are selected primarily from applied mechanics. Among topics included are Fourier series, separation of variables, Bessel functions, Fourier and Laplace transforms, Green's functions and complex function theories. Also covered are advanced topics such as Riemann–Hilbert techniques, perturbation methods, and practical topics such as symbolic computation. Engineering students, who often feel more awe than confidence and enthusiasm toward applied mathematics, will find this approach to mathematics goes a long way toward a sharper understanding of the physical worl

This book provides applied biologists and ecologists with the mathematical tools they need to understand the ever increasingly mathematical and complex area of population ecology.

The late Professor G. N. Watson wrote his monumental 1995 treatise on the theory of Bessel functions with two objects in view. The first was the development of applications of the fundamental processes of the theory of complex variables; and the second was the compilation of a collection of results of value to mathematicians and physicists, who encounter Bessel functions in the course of their researches. The completeness of his theoretical account, combined with the wide scope of the practical examples and the extensive numerical tables, have resulted in a book which is indispensable to pure and applied mathematicians, as well as to physicists.

This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potent

Recent advances in establishing the nature and scope of estimators in econometrics have shed more light on the importance of instrumental variables. In this book, the authors argue that such methods may be regarded as a strong organizing principle for a wide variety of estimation and hypothesis testing problems in econometrics and statistics. In support of this claim they present and develop the methodology of instrumental variables in its most general and explanatory form. They show, for instance, that techniques commonly used to handle simultaneity and related problems can be reduced to one of two generic variables of instrumental variables estimators, allowing them to explore further the conditions under which different proposed estimators are efficient.